There has been a growing interest in implementing state-resolved models for flowfield calculations of high-speed reentry applications that are characterized by regions of strong nonequilibrium. To this end, the present work provides a technique to rigorously compute transport collision integrals for vibrationally excited molecules. Collision dynamics calculations are extended to include state-to-state (StS) effects, and vibrationally resolved transport collisional quantities including scattering angles, cross sections, and collision integrals are computed for the $\mathrm{O}+{\mathrm{O}}_2$ system using potential energy surfaces (PESs) by Varga et al. [J. Chem. Phys. 147, 154312 (2017)]. From the nine surfaces provided by Varga et al., the “surface-averaged” collision integrals are computed for the oxygen system, and Gupta-Yos-style fits to the data are provided. It is found that the StS collision integrals depend not only on the vibrational state of the molecule, but also on the spin and spatial degeneracy associated with the PES that governs the interaction. Comparison of the collision integrals from the Varga et al. surfaces with those generated from the Varandas and Pais PES [Mol. Phys. 65, 843 (1988)] shows significant differences at highly excited vibrational states. The highly attractive nature of the Varandas and Pais surface leads to a monotonic increase in the collision integral values with vibrational excitation of ${\mathrm{O}}_2$, while the surface-averaged state-based collision integral values computed from the comparatively repulsive Varga et al. set of surfaces generally increase with vibrational excitation for temperatures up to 6000 K, and decrease with vibrational excitation at higher temperatures. Additionally, due to this nontrivial dependence of the collision integrals on the vibrational state of ${\mathrm{O}}_2$, simple empirical models are found to be unable to correctly estimate vibrational state-based collision integrals. Differences as high as 80% are obtained between the model predictions and values computed directly from the underlying PES. Evaluation of vibrationally resolved viscosity and translational thermal conductivity for the $\mathrm{O}+{\mathrm{O}}_2$ system under equilibrium conditions indicate that both these transport coefficients depend on the vibrational excitation of ${\mathrm{O}}_2$, with the contribution of the excited vibrational states increasing with rising temperature.

中文翻译：

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O + O2系统的状态解析运输碰撞积分

对于以强非平衡区域为特征的高速重入应用流场计算，实施状态解析模型的兴趣日益浓厚。为此，本工作提供了一种技术，可以为振动激发的分子严格计算运输碰撞积分。碰撞动力学计算被扩展为包括状态对状态（StS）效应，并且为该碰撞计算了包括散射角，横截面和碰撞积分在内的振动分解的运输碰撞量。$\mathrm{Ø}+{\mathrm{Ø}}_2$Varga等人使用势能面（PES）的系统。[ J. Chem。物理 147，154312（2017）]。从Varga等人提供的9个表面中。，为氧气系统计算“表面平均”碰撞积分，并提供与数据的Gupta-Yos风格拟合。发现StS碰撞积分不仅取决于分子的振动状态，还取决于与控制相互作用的PES相关的自旋和空间简并性。Varga等人的碰撞积分的比较。表面由Varandas和Pais PES产生[ Mol。物理 65岁，843（1988）]显示了在高激发振动状态下的显着差异。Varandas和Pais表面的极具吸引力的特性导致碰撞积分值随着振动激励的增加而单调增加。${\mathrm{Ø}}_2$，而根据相对排斥的Varga等人计算出的基于表面平均状态的碰撞积分值。当温度高达6000 K时，一组表面通常随振动激发而增加，而在较高温度下，随着振动激发而减少。此外，由于碰撞积分对振动状态的非平凡依赖，${\mathrm{Ø}}_2$，发现简单的经验模型无法正确估计基于振动状态的碰撞积分。在模型预测和直接从基础PES计算得出的值之间获得高达80％的差异。振动解析粘度和平移导热系数的评价。$\mathrm{Ø}+{\mathrm{Ø}}_2$ 平衡条件下的系统表明，这两个输运系数都取决于振动激励。 ${\mathrm{Ø}}_2$，随着温度的升高，激振状态的贡献也随之增加。